Explain walks, paths and circuits with the help of examples.

Sure! I can explain walks, paths, and circuits with the help of examples.

A walk in a graph refers to a sequence of vertices and edges that are connected in a specific order. It can be a simple walk, where no vertex or edge is repeated, or it can be a closed walk, where the starting and ending vertices are the same.

For example, consider the following graph:

A -- B -- C -- D

A walk in this graph could be A-B-C-D, where we start at vertex A, move to vertex B, then to vertex C, and finally to vertex D.

A path, on the other hand, is a type of walk where no vertex is repeated. It is a simple walk with no repeated vertices.

Continuing with the same example, a path in this graph could be A-C-D, where we start at vertex A, move to vertex C, and then to vertex D. Notice that we skipped vertex B in this path.

Finally, a circuit is a closed walk where no edge is repeated, except for the starting and ending edge, which are the same.

In our example graph, a circuit could be A-B-C-D-A, where we start and end at vertex A, and visit all the vertices in between without repeating any edge.

I hope this explanation helps you understand walks, paths, and circuits in graphs!